Question

Given the line y=3x+4 write the equation of a line in slope intercept form which is perpendicular to the given line and goes through 2,1

Answer 1

Answer:

$y_{}=-\frac{1}{3}x+\frac{5}{3}$

Explanation:

Given the line y=3x+4

Comparing it to the slope-intercept form, y=mx+b

• Slope of y=3x+4 = 3

Two lines are perpendicular if the product of their slopes is -1.

Let the slope of the new line = m

$\begin{gathered} 3m=-1 \\ m=-\frac{1}{3} \end{gathered}$

The slope of the perpendicular to the given line that goes through (2,1) is:

$\begin{gathered} y-y_1=m(x-x_1) \\ y-1=-\frac{1}{3}(x-2_{}) \end{gathered}$

We then write it in slope-intercept form.

$\begin{gathered} y_{}=-\frac{1}{3}x+\frac{2}{3}+1 \\ y_{}=-\frac{1}{3}x+\frac{5}{3} \end{gathered}$

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